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Axiom ax-mulf 10054
Description: Multiplication is an operation on the complex numbers. This deprecated axiom is provided for historical compatibility but is not a bona fide axiom for complex numbers (independent of set theory) since it cannot be interpreted as a first- or second-order statement (see http://us.metamath.org/downloads/schmidt-cnaxioms.pdf). It may be deleted in the future and should be avoided for new theorems. Instead, the less specific ax-mulcl 10036 should be used. Note that uses of ax-mulf 10054 can be eliminated by using the defined operation (𝑥 ∈ ℂ, 𝑦 ∈ ℂ ↦ (𝑥 · 𝑦)) in place of ·, from which this axiom (with the defined operation in place of ·) follows as a theorem.

This axiom is justified by theorem axmulf 10005. (New usage is discouraged.) (Contributed by NM, 19-Oct-2004.)

Assertion
Ref Expression
ax-mulf · :(ℂ × ℂ)⟶ℂ

Detailed syntax breakdown of Axiom ax-mulf
StepHypRef Expression
1 cc 9972 . . 3 class
21, 1cxp 5141 . 2 class (ℂ × ℂ)
3 cmul 9979 . 2 class ·
42, 1, 3wf 5922 1 wff · :(ℂ × ℂ)⟶ℂ
Colors of variables: wff setvar class
This axiom is referenced by:  mulnzcnopr  10711  mulex  11869  rlimmul  14419  mulcn  22717  iimulcn  22784  dvdsmulf1o  24965  fsumdvdsmul  24966  cncvcOLD  27566  rmulccn  30102  xrge0pluscn  30114
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